Energy exponents and corrections to scaling in Ising spin glasses

J.-P. Bouchaud, F. Krzakala, and O. C. Martin
Phys. Rev. B 68, 224404 – Published 3 December 2003
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Abstract

We study the probability distribution P(E) of the ground-state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system’s volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean-field diluted spin glasses having ±J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite-dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent θDW. We also show how a systematic expansion of θDW in powers of ed can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

  • Received 6 December 2002

DOI:https://doi.org/10.1103/PhysRevB.68.224404

©2003 American Physical Society

Authors & Affiliations

J.-P. Bouchaud1, F. Krzakala2,3, and O. C. Martin1,2

  • 1Service de Physique de l’État Condensé, Orme des Merisiers—CEA Saclay, 91191 Gif sur Yvette Cedex, France
  • 2Laboratoire de Physique Théorique et Modèles Statistiques, Bâtiment 100, Université Paris-Sud, F-91405 Orsay, France
  • 3Dipartimento di Fisica, INFM, SMC, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy

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Vol. 68, Iss. 22 — 1 December 2003

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